Antibiotic resistance evolution is commonly mediated by missense mutations in a single protein (e.g. antifolate resistance mutations are often in dihydrofolate reductase, quinoline resistance mutations are often in DNA gyrase, rifamycin resistance mutations are often in RNA polymerase). This fact draws attention to the mechanistic details of protein evolution: how do individual mutations influence protein structure and function so as to allow pathogenic microbes to survive in the presence of the drug? b-lactam antibiotics (e.g. penicillin and the cephalosporins) represent 65% of the world antibiotic market [65], and the TEM serine b-lactamases are the chief source of clinical, plasmid mediated b-lactam resistance [64]. The biochemical and biophysical determinants of TEM b-lactamase activity are experimentally accessible [e.g. 2, 7], making this an ideal model system in which to dissect the mechanistic process of protein evolution. The present proposal is to use a novel, geometric model of protein evolution to do just this. This work simultaneously advances the field of evolutionary genetics, which is now beginning to move from statistical tests for evidence of natural selection to questions of molecular mechanism [4]. Recent work has highlighted the fact that to be successful a protein must perform its function (e.g. enzymes must catalyze their chemical reactions) but simultaneously it is under stabilizing selection (i.e. must fall within narrow tolerances) for structural traits such as folding stability, aggregation and degradation potentials and likely others. Moreover, most missense mutations exhibit pleiotropy, meaning that they perturb more than one such trait. These biophysical and biochemical considerations motivate a picture of protein evolution in which adaptation is a succession of mutations, each with net beneficial effect that act by substantially improving some traits while modestly degrading others [5]. This model decomposes protein evolution into its mechanistically most proximal components, and is formally analogous to a geometric model of adaptation first proposed by RA Fisher [6]. In the present proposal, this theory is extended to allow inference into mutational mechanisms of action based on their effect on organismal fitness. This theoretical innovation is important because measuring mutational effects on fitness is often far more practical than is the identification of their biochemical and biophysical mode of action. This theory will then be applied to a novel panel of mutations in TEM b-lactamase, whose effect on drug resistance will be characterized as a proxy for fitness. Finally, capitalizing on the experimental tractability of TEM b- lactamases, predictions made about these b-lactamase mutations using this theory will be validated via the bottom-up, biochemical and biophysical characterization of the mechanism of these same mutations.